"out of memory" error for defining variable and constraint
AnsweredThere is a constraint that I should implement in my project which is x[i, j, s, t] + x[j, k, s, t] ) <= 1 for (i, j) in E0 for (j, k) in E0 for (s, t) in D_s_t, for this constraint, I define a variable like the following:

Based how you described the problem, I assume there should be one variable for every combination of an element/pair from \(\texttt{E0}\) and an element/pair from \(\texttt{D_s_t}\). Is that correct? This would result in \(\texttt{E0} \cdot \texttt{D_s_t}\) variables. However, your code adds \(2 \cdot \texttt{E0}^2 \cdot \texttt{D_s_t}\) variables to the model. Many of these variables are duplicates of each other (meaning they use the same indices and have the same name), because you iterate over \(\texttt{E0}\) in its entirety twice.
Instead, I would define your variables using Model.addVars():
x = model.addVars(E0, D_s_t, vtype=gp.GRB.BINARY, name="x")
This creates a variable for every combination of an element in \(\texttt{E0}\) and an element in \(\texttt{D_s_t}\). The variables will be indexed and named accordingly.
Regarding your constraints:
x[i, j, s, t] + x[j, k, s, t] <= 1 for (i, j) in E0 for (j, k) in E0 for (s, t) in D_s_t
Are you trying to model the following?
\begin{align*}x_{i,j,s,t} + x_{j,k,s,t} \leq 1 \qquad \forall (s, t) \in \texttt{D_s_t},\ (i, j, k) : (i, j) \in \texttt{E0},\ (j, k) \in \texttt{E0}\end{align*}
If so, then depending on how exactly you define \(\texttt{E0}\) and \(\texttt{D_s_t}\), this can be accomplished with code similar to the following:
E0 = gp.tuplelist(E0)
for s, t in D_s_t:
for i, j in E0:
for _, k in E0.select(j, "*"):
m.addConstr(
x[i, j, s, t] + x[j, k, s, t] <= 1,
name=f"limit[{i},{j},{k},{s},{t}]",
)0 
Thank you for your comment, it works well. However, I have another question that is related to the previous question. I have several constraints related to x an example:
I have two constraints on x with two different variables:
1. x[i, j , s, t] + x[j, k, s, t] <= 1 for each (s, t) in D_s_t for each (i, j) in E0 for each (j, i) in E0
2. x[i, j, s, t] * v[s, t] <= 10 for each (s, t) in D_s_t for each (i, j) in (E + E1 + E2)
how should I define x?
should I implement the x = model.addVars(E0 + E + E1+ E2, D_s_t, type = gp.GRB.BINARY, name = ''x"), and sometimes I've got an error duplicate Var because two sets (E0) and (E + E1 + E2) may have duplicate value.
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If you intend to use the same \( x \) variable for each \((i, j)\) in \(\texttt{E0}\) that also exists in \(\texttt{E + E1 + E2}\), you could define the \( x \) variables using only the unique elements of the union of these lists. For example:
U = list(set(E0 + E + E1 + E2))
x = m.addVars(U, D_s_t, vtype=gp.GRB.BINARY, name="x")0 
Thank you for your comment. It perfectly works.
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